which angles of the transformation figures have the same measure as

The area of the isosceles triangle is 60 square units

The formula for area of an isosceles triangle is expressed as;

Area = bh/2

Where;

Now, let's find the height of the triangle.

Using Pythagorean theorem, we have;

13^2 = 5^2 + h^2

Find the square

169 = 25 + h^2

collect like terms

169- 25 = h^2

h^2 = 144

Find the square root of both sides

h =√ 144

h = 12

Let's find the area

Area = 10 × 12/2

Area = 120/2

Area = 60 square units.

Thus, the area of the isosceles triangle is 60 square units

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Answer:

The ray extends infinitely in one direction.

Step-by-step explanation:

It starts at the point and the arrow at the ends mean it extends in that direction away from the point infinitely.

Answer:

Step-by-step explanation:

n x 5

Answer:

disagree because the outcome of the problem would be incorrect

The difference between the measures of center is equal to the measure of variation.

The IQR of the given box plot:

Q1 = 10

Q3 = 18

IQR = Q3 − Q1 = 18 − 10 = 8

Median = 15

Q1 = 4

Q3 = 12

IQR = Q3 − Q1 = 12 − 4 = 8

The difference between the measures of center as a multiple of the measure of variation:

Median of first data set - median of the second data set

IQR = 15 − 7 / 8

= 1

Therefore, the difference between the measures of center is equal to the measure of variation.

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Express the difference between the measures of center as a multiple of the measure of variation.

Given is a box plot for the number of questions attempted in subject 1 by different students.

The domain of the relation is {1, 2, 3, 4, 5} and the range of the relation is {0.75, 1.50, 2.25, 3.00, 3.75}

As per the question statement, the total cost for cars entering President George Bush Turnpike at Beltline Road is related to the number of cars entering the turnpike at Beltline Road. The costs of different numbers of cars entering the turnpike at Beltline Road are as follows: 1 car, $0.75; 2 cars, $1.50; 3 cars, $2.25; 4 cars, $3.00; 5 cars, $3.75.

Before solving the question we need to know what is domain and range basically.

Ordered pair : {(1,0.750 , (2,1.50) , (3,2.25) , (4,3.00) , (5,3.75)}

Domain is the set which consists of all the first elements of all the ordered pair of the given relation, therefore Domain is {1, 2, 3, 4, 5}.

Range is the set which consists of all the second elements of all the ordered pair of the given relation, therefore Range is {0.75,1.50,2.25,3.00,3.75}

And yes, the given relation is also a function because as the number of cars increases the total cost is also increasing but gradually with a constant value.

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The area of the trapezoid is 24cm².

It should be noted that the area of a trapezoid is calculated as:

Area = h × (a + b//2

where h = height

Area = 4 × (4 + 8)/2

Area = 4 × 12/2

Area = 4 × 6

Area = 24cm²

The area is 24cm²

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The average payment will be $611.64.

It should be noted that average means mean. This implies that we will add the numbers and then divide.

This will be:

= ($23.42 + $14.95 + $276.50 + $219.93 + $76.84) / 5.

= $611.64

Therefore, the average payment will be $611.64.

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Answer:

All these added amount to $611.64, yes.

However, to find average, you then divide by 6.

Which equals; $101.94.

That is the average payment.

Step-by-step explanation:

Hope it helps.

Answer:

the number of times he washes the car

Step-by-step explanation:

[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-1})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{3}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{- \cfrac{3}{4}}(x-\stackrel{x_1}{8}) \implies y +1= -\cfrac{3}{4} (x -8) \\\\\\ y+1=-\cfrac{3}{4}x+6\implies {\LARGE \begin{array}{llll} y=-\cfrac{3}{4}x+5 \end{array}}[/tex]

Answer:

[tex]y_e = -\frac34x + 5[/tex]

Step-by-step explanation:

The equation of a line, if given its slope and one point that it passes through, is given by the formula [tex]y - y_1 = m(x - x_1)[/tex].

Therefore, we can substitute [tex]m = -\frac34[/tex], [tex]x_1 = 8[/tex] and [tex]y_1 = -1[/tex] into the formula above.

[tex]y - (-1) = -\frac34(x - 8)\\\\\to y + 1 = -\frac34x + 6\\\\\to y = -\frac34x + 5[/tex]

Line that passes through (0,-6) and (2,-4)

[tex]y = mx + c \\ m = \frac{ - 6 + 4}{0 - 2} = \frac{ - 2}{ - 2} = 1 \\ c = y - mx = - 4 - 1(2) = - 6 \\ y = x - 6[/tex]

If the third point (-3,-8) belongs to this line, then it must satisfy its equation and be collinear to the other two points, if not, then these points are not collinear, check:

[tex] - 8 = - 3 - 6 \\ - 8≠ - 9 \\ so \: nopeeee[/tex]

According to the given  the given  logarithm log₃ 1/9 the value is = -2

Logarithmic functions are significant due of their link to exponential functions. Logarithms are useful for solving exponential equations and investigating the properties underlying exponential functions.

log₃ 1/9

Can be written as:

log₃ (1/9) = x

using the log definition in exponential form. if x and b are positive real number and b dose not equal 1 then  log_b (x) = y is equivalent to b^y = x.

3^x = 1/9

creating equivalent expression in the equation that all have equal base.

3^x = 3^-2

if the base are the same, two expression are only equal if the exponential are also equal

x = -2

the variable x is equal to -2

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Answer is the coordinates of endpoint F(6, 4).

In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.

let coordinate of F is (x,y).

4= (x + 2)/2

8= x +2

x = 6

6= (y +8)/2

12 = y + 8

y = 4

Answer is the coordinates of endpoint F(6, 4).

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Answer:

I think the answer is

1/2x + 5

Step-by-step explanation:

The simplest form of the expression [tex](\frac{x^{4}}{x^{-1}} )^{\frac{-1}{5} }[/tex] is [tex]\frac{1}{x}[/tex].

The simplest form of a fraction is one with a reasonably prime denominator and numerator. It indicates that, except for 1, there is no common factor between the fraction's numerator (upper portion or top) and denominator (lower part or bottom).

A fraction is a number that has been expressed as a quotient by dividing the numerator by the denominator. Both are integers in a simple fraction. In a complex fraction, a fraction can be found in either the numerator or the denominator.

An expression is made up of a number, a variable, or a combination of a number, a variable, and operation symbols. Two expressions joined by an equal sign form an equation.

Consider the expression,

[tex](\frac{x^{4}}{x^{-1}} )^{\frac{-1}{5} }[/tex]

Now we know,

[tex]x^{-1}=\frac{1}{x}[/tex]

Therefore,

[tex](\frac{x^{4}}{x^{-1}} )^{\frac{-1}{5} } =(\frac{1}{\frac{x^4}{x^{-1}} })^{\frac{1}{5} }[/tex]

[tex](\frac{x^{4}}{x^{-1}} )^{\frac{-1}{5} } =(\frac{x^{-1}}{x^4})^{\frac{1}{5}[/tex]

[tex](\frac{x^{4}}{x^{-1}} )^{\frac{-1}{5} } =(\frac{1}{x \times x^4})^{\frac{1}{5}[/tex]

Using the exponential rule,

[tex]n^{b} \times n^{a} = n^{a+b}[/tex]

[tex](\frac{x^{4}}{x^{-1}} )^{\frac{-1}{5} } = (\frac{1}{x^{5}} )^{\frac{1}{5}[/tex]

[tex](\frac{x^{4}}{x^{-1}} )^{\frac{-1}{5} } = \frac{1}{x^{5 \times \frac{1}{5} }}[/tex]

[tex](\frac{x^{4}}{x^{-1}} )^{\frac{-1}{5} } = \frac{1}{x}[/tex]

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the answer to the given logarithm expression is log₃ 125 = 3

Another technique to explain exponents in mathematics is through logarithms. A base number's logarithm equals another number.

The power's inverse function is the logarithm. For instance, log10 100 = 2 if 102 = 100. A power to which a number must be increased in order to achieve another value is referred to as a logarithm.

This is the most practical method for displaying enormous numbers. Logarithms have several important properties that prove that multiplication and division of logarithms can  be written in terms of addition and subtraction logarithms. A second name for the common logarithm is the base 10 logarithm.. This is represented as log10 or simply log. The base 10 logarithm is another name for the common logarithm. The common logarithm specifies the number of times the number 10 must be multiplied in order to produce the desired result.. We need to evaluate log₃ 125

Using the property

logₐ (mⁿ) = n logₐ m

125 = 5³log₃ 125 can be written as log₃ 125= 3 log₅ 5

We know that logₐ a = 13 log₅ 5= 3

Therefore, we calculated the logarithm, which is log₃ 125 = 3

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The intensity level of the earthquake in New Madrid, Missouri in 1812 was about 1.6 times less than the intensity level of the earthquake Valdivia, Chile, in 1960.

We use the following formula for comparing the intensity level of earthquakes-

Log (i1 / i2) = M1 - M2

where i = intensity level determined by a seismograph

M = magnitude on a Richter scale.

Now, from the given information-

magnitude of earthquake in New Madrid = 7.9

Thus, M1 = 7.9

Then intensity of the earthquake in New Madrid = i1

magnitude of earthquake in Chile = 9.5

Thus, M2 = 9.5

Then intensity of the earthquake in Chile = i2

⇒ log (i1 / i2) = 7.9 - 9.5

log (i1 / i2) = -1.6

This means that the intensity level of the earthquake in New Madrid, Missouri in 1812 was about 1.6 times less than the intensity level of the earthquake Valdivia, Chile, in 1960.

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After thoroughly calculating the simplifying the expression 164[3+2+ (9-7)] is   1148

An expression in mathematics is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)

You can think of expressions as being similar to phrases. A phrase in language may contain an action on its own, but it does not constitute a complete sentence.

The following are some examples of expressions and word phrases that they relate to:

Formula: 3 + 7

Expressions and equations are different from one another because an expression consists of a combination of numbers, variables, and operation symbols, whereas an equation consists of two different expressions joined together by an equals sign. This shows that the expression's two sides have the same value.

Simplification of the expression 164[3+2+ (9-7)]

⇒ 164[3+2+ (9-7)] =

⇒ 164[5+(2)] =

⇒ 164[5+(2)]

⇒ 164(7)

⇒ 1148

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In linear equation, 40100  is the total height of Mauna Loa .

What in mathematics is a linear equation?

the total height of Mauna Loa

26400 +13700 = 40100

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The complete question is -

Mauna Loa depresses the sea floor, resulting in 26400 more feet added to its height. If Mauna Loa is 13700 ft tall. What is the total height of Mauna Loa?

Let x be the number of weeks passed.

Denote by J(x) the money with Joe.

Denote by B(x) the money with his brother.

Denote by s(x) the money they raised together.

[tex]J(x)=assets+money \: raised \\ J(x)=170 + 20x[/tex]

[tex]B(x)=assets+money \: raised \\ B(x)=80+40x[/tex]

If we want Joe's brother to have more money at the x week, then B(x) has to be greater than J(x)

[tex]B(x) > J(x) \\ 80 + 40x > 170 + 20x \\ 40x - 20x > 170 - 80 \\ 20x > 90 \\ x > \frac{90}{20} \\ x > 4.5 \: \: \: so \: \: \: x = 5[/tex]

We know that at the 5th week, Joe's brother will have raised more money than Joe, but how much money did they raise together by then?

[tex]s(x) = B(x) + J(x) \\ s(5) = B(5) + J(5) \\ s(5) = 80 + 40(5) + 170 + 20(5) \\ s(5) = 80 + 200 + 170 + 100 \\ s(5) = 550 \: dollars \: raised[/tex]

Answer:

0.0035

Step-by-step explanation:

In front of the decimal point is the ones place. After that is the tenths place, hundredths place, and then thousandths place.

Answer:

3,000000

Step-by-step explanation:

10^6=1000000

1000000x6=6000000

6000000/2=3000000

The problem does not mention the height of S. Mr. Watkins, so we are just going to assume its from his feet.  

So, i made this drawing to represent him and the tree, at a distance of 10 meters looking up at a 25* angle.

I marked the opposite side, adjacent side, and hypotenuse.

x is angle where you are "looking" from.  I.E., from the POV of mr watkins.

sin(x) = opposite/hyp

cos(x) = adj/hyp

tan(x) = opp/adj

So, we have an unknown side which is the opposite side, represented by length x.

The side adjacent is 10 meters.

The angle from him is 25 degrees.

What deals with adjacent and opposite?  Tangent.

Tan(25) = x/10

Solve for x.

10tan(25) is the height of the tree = 4.66

The height of the tree is 5 meters.

The domain of the function h(x) = x² - x - 12 when the function operation f(x) = g(x) is performed is ( - ∞ , ∞ ).

A domain is a collection of potential input values. All input values visible on the x-axis make up the graph's domain. The collection of potential output values represented on the y-axis is known as the range.

Consider the two functions,

f(x) = x - 4 and g(x) = x² - 16

The function operation f(x) = g(x).

g(x) - f(x) = h(x)

x² - 16 - ( x + 4 ) = h(x)

h(x) = x² - x - 16 + 4

h(x) = x² - x - 12

The collection of input or argument values for which a function is actual and defined is known as its domain.

So, the domain of the function h(x) is ( - ∞ , ∞ ) or - ∞ < x < ∞.

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Answer: they will get 27 each and their will be 13 left over

Step-by-step explanation:

The corresponding growth factor of +500% is 6

The formula for the annual rate of change is

                            1 ± r           (1)

where r = rate of change

and ± sign depends upon whether it is a growth or decay factor. If it is growth factor then it is plus sign otherwise negative sign.

According to the question we have been given the growth that is +500%. Since there is plus sign therefore it is a growth factor.

Thus, r = + 5

Putting this value in equation (1) we get

     = 1 + 5

     = 6

Hence the corresponding growth factor of +500% is 6

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The subtraction equation is 100 + (-45.43) = 54.57 and the number line is as shown in the attachment.

We want to write a subtraction equation with a difference of 54.57. The difference of 54.57 can be gotten from;

\100 + (-45.43) = 54.57

Now, if we draw the number above in a number line, it would be exactly as shown image attached. By careful observation, the difference is between 45 and 100 which are both whole numbers, but the exact difference as seen in the the red space.

Therefore, the subtraction equation is 100 + (-45.43) = 54.57

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